Are these correct:1) Anyone who saw and recognized him should have reported him to the police, but no one did. I am sure many people saw him and knew who he was, but no one dared report him to the police.2) Anyone who went up this sidewalk before me should have picked up that banana skin. This is a crowded street and a lot of people saw it before I did, and none of them picked it up.

So, in the U.K., they say, "Let's make like a banana skin and split." Doesn't sound quite right to me . . .

Shelley : irrespective of the peel or skin question , what does "Let's make like a banana skin and split" supposed to be or mean? I have not heard the expression before.

But this topic has me thinking. So thoughts:

OED
PEEL
a. The rind, skin, or outer covering of a fruit, a vegetable, or (occasionally) a plant; esp. the skin of a citrus fruit, often used as a flavouring (cf. zest n.1 1).

SKIN
10. An outer layer or covering.
a. The outer covering of certain fruits and vegetables; the peel or rind; (also) the bark or rind of a tree or plant.
banana, orange, potato skin, etc

1 I use skin and peel differently.
2 I peel a banana, I don't peel a rabbit.
3. I don't skin a banana, I do skin a rabbit.
4. A banana has skin, I don't think it has peel except I might remove the peel.
5. The skin of a banana, once removed but still joined at the stalk, I would probably call the skin. A piece (maybe a lobe) of skin intentionally removed is peel or a peeling.
6. I risk stepping on banana skin or on banana peel.
7. An orange has skin.
8. I would add orange peel to the recipe. I wouldn't add orange skin. I only want the peel, not the skin.

Well, I'll stop now, but that hasn't resulted in a clear set of rules.

Good points, Tony. I think there a couple of things we can narrow down, at least for UK usage:

Generically, we usually (always?) "peel" fruit and vegetables and "skin" animals.

While the outer covering of a piece of fruit or a vegetable is still attached, it is usually referred to as the "skin".

Once removed or during removal, the outer covering is usually referred to as "peel" (or, with vegetables such as potatoes, "peelings".

Bananas in particular do not follow this pattern.

I strongly suspect that the reason for the difference with bananas is twofold. Firstly, the skin of a banana is usually removed in one piece (or the banana is eaten while leaving the skin intact). Secondly, we do not use an implement to peel (sic) a banana (even with an orange, for instance, we often use a fruit knife or our finger nails to remove the skin (peel?). I think it is the former of these (the completeness of the skin) that motivates the use of "skin" in the UK.

But that which cartoon characters and politicians step on (literally or metaphorically) is, in the UK, always a banana skin as far as I am aware.

And Shelley, that use of "split" is known in the UK, but has never been particularly widespread. So the expression "let's make like a banana and split" is pretty well unknown here (and I for one have never heard the version with "banana peel".)

Ed.: It occurs to me that tomatoes also always have "skin(s)" and not "peel". Which is not predicted by my theory above.

. . . what does "Let's make like a banana skin and split" supposed to be or mean?

Sorry, tony h -- if I'd said it right (like Phil White did above), it might have made more sense. Making like a banana and splitting is a reference to a "banana split", an over-indulgence involving:

a banana, split in half, lengthwise, as the base,
topped with 3 scoops (usually) of ice cream,
whipped cream,
fudge (or other) sauce,
nuts and
a maraschino cherry.
[one can reverse the order of the sauce and whipped cream]

At least that's what I've always thought, until this conversation. The skin of a banana CAN split, so maybe that's all that's going on here. Or, I suppose, one could say, "Let's make like a banana and peel", as in peeling rubber (stepping on the accelerator so heavily, that you leave a black stripe of tire on the pavement, like burning rubber).
I don't know . . . I'm confused. But anyway, where I come from, bananas are wrapped in peels, not skins.

I'm not sure if there is any science behind it, but I seem to differentiate then by thickness (or, at least amount of protection they offer) Tomatoes, grapes, onions and peaches have skins. Potatoes, apples, oranges, and bananas have peels. I know that some people say that an orange has a rind but I usually reserve rind for tougher coverings...cantaloupes, cheeses and bacon (ok, bacon rind is actually skin...but it's a pretty thick skin...isn't that a pithy?)